Fluid–Solid Interaction: Acoustic Scattering by a Smooth Elastic Obstacle
C. J. Luke, Paul A. Martin · SIAM Journal on Applied Mathematics · 1995
A bounded three-dimensional elastic obstacle is surrounded by an unbounded inviscid compressible fluid. Acoustic waves are scattered by the obstacle; the problem is to find the scattered waves and the response of the obstacle. This problem is formulated mathematically; existence and uniqueness theorems are proved. Various systems of boundary integral equations over the interface between the fluid and the solid are derived and analysed. These systems include a system obtained by a straightforward direct method and a smaller system for a single vector field.